Why is it so important to warm up before singing?  For the same reasons that you would stretch before running or  engaging in other major muscular activity.

The muscles of the larynx are small.  The traditional description of the vocal folds is that they are the length of the pink part of your pinkie fingernail.  They exist inside three cartileges that all together are about the size of a walnut.  The muscles that move the larynx cartileges are probably shorter than their names. Everything about the larynx is small except for the muscles around it.

The tongue and jaw muscles are strong.  So are the neck and shoulder muscles, and while they do not directly affect one's singing, many singers find that tension in the neck and shoulders transfers into their singing voice.  It is only reasonable to organizie one's physical being before starting to sing, and it doesn't take a long time, although a long and peaceful warm up can be very comfortable.

Most singers like to start by placing their bodies in a good singing posture, then by breathing a few times in the manner in which they breathe for singing -- low and slow are ususally catch words for a singer's breath.  Then a short exercise that goes up and down maybe a 5th or so, moving up by half steps mostly within the middle voice.  The total range covered would be about an octave.  The next step is often a scale exercise of about an octave, again moving up and down by half steps, but this time going a little higher and a little lower.  Finally an arpeggio exercise to make all the technical adjustments a bit faster because one moves now by skip instead of by step.  It takes about five to ten minutes, and the body is ready to sing.

A lot of singers have other fun warm ups that they like.  Lip trills, slides, glides, and even gargling with pitch are some I've encountered.  I have no problem with all these things.  Singers always have to find what makes them feel relaxed and ready.  Particularly when one is in a pressured situation, perhaps starting lessons with a new teacher or warming up for an audition, anything that helps a singer release physical and mental tensions is what s/he should do. 

Most of the time a singer is warming up before a practice session.  Most good singers won't start a practice session with their hardest music.  Generally singers will start with a less demanding piece and move on to music that makes greater vocal demands.  Sometimes the hard music comes first, but in that case generally the singer is taking a small portion of the piece that needs work and working on it with less than full voice.  Singers will continue to feel more comfortable as they sing, and at some point will be ready to make a full effort.

Protecting your voice has to be important to you as a singer because replacement parts just are not available.  Wear and tear on the voice is cumulative.  Although it's possible to come back from vocal damage, it's far better to avoid damage as much as possible.  Adalina Patti, a diva of the 19th century, used to refuse to sing High C in rehearsals because she believed that she had only a finite number of them.  She didn't waste them on rehearsals.  Maybe her attitude is a bit much, but one must agree that she took her responsibility seriously.

Students often feel that they should sacrifice their voice for a performance because others are depending on them.  I've done it, and so has every singer I know.  Just try not to do it too often.  Warm up and take care.